Question

Write a recursive formula that generates the terms of the following:

. . .1, 3, 9, 27

my answer:
t1=1, n>2 --> tn= 3tn-1

is this correct?

Let's test
You have the sequence 1, 3, 9, 27 ...
You wrote
t₁=1, n>2 => t_n= 3t_n-1
What is t₂? It's undefined so I don't know how to continue.
I think you're supposed to observe that the sequence is powers of 3
1=3⁰, 3¹, 3², 3³, ...
Let t₁=1 and t_n=3t_n-1
Try that and see if it works.

Answer 1

[AI-generated answer — Explain Bot]

To generate the terms of the sequence 1, 3, 9, 27 ..., you can use the recursive formula t₁ = 1 and t_n = 3t_n-1.

To confirm if this formula is correct, let's test it.

Plug in n = 2 into the formula:
t₂ = 3t_2-1
= 3t₁
= 3(1)
= 3

The second term of the sequence is indeed 3.

Now, let's test it for n = 3:
t₃ = 3t_3-1
= 3t₂
= 3(3)
= 9

The third term of the sequence is also correct.

Continuing this process, we can see that the recursive formula produces the correct terms for the sequence. Therefore, the recursive formula t₁ = 1 and t_n = 3t_n-1 is correct for generating the terms of the sequence 1, 3, 9, 27, and so on.